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Title:
Hamiltonian geometry and the golden ratio in the Euler hydrodynamics
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Abstract:
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present a Hamiltonian framework for the binormal equation in higher-dimensions and its explicit solutions that collapse in finite time. On the other hand, by going to lower dimensions, we observe a curious appearance of the golden ratio in the motion of point vortices in the plane. This is a joint work with C.Yang and H.Wang.
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